A summary of the rulesEach year, starting with 1915 (supposedly 1901, but the map is more like later in Europe's history), with several phases per year.
Spring Movement: Units move, or do non-movement things.
Spring Retreat/Disbandment Phase: Failed attacks resolve with retreating or dying.
Autumn: Like Spring.
Winter Build/Disband: You either build or disband fleets or armies until the number of your units equals the number of your supply centers.
Units can move one territory per movement phase--for instance, from the Gulf of Bothnia to the Baltic Sea, from Venice to Trieste, or from London's coast to the North Sea. The exception to this rules is convoys--if you have a line of ships reaching from one land territory to another, and all ships work on convoying, you can move an army directly between them. Only one unit can be in any one territory.
Obviously enough, attacking is pretty important. However, defenders have a pretty big advantage in Diplomacy. If one unit defends and one unit attacks, the attacker is simply "bounced"--it will retreat in the Retreat/Disband phase. In order to win, you need to support your attack with other units, or have allies do the same. Of course, you need to agree on who's attacking and who's supporting--if two units attempt to enter the same territory with equal or no support, both are bounced.
Aside from helping a convoy, supporting, or of course moving, a unit in the Movement phase can simply hold, defending its territory.
The first to reach 18 supply centers wins...because once you have half the map, you can crush the other half easily.
If any rules have been forgotten, added, muddled, or screwed up, inform me thusly and I will correct the error.